The generator matrix

 1  1  1  1  1  2  1  1  1
 0 12  0  0  0  8  4  8  0
 0  0 12  0  0  4  4 12  0
 0  0  0 12  0  4  0  8  0
 0  0  0  0 12  4  8  4  0

generates a code of length 9 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+22x^4+62x^5+67x^6+108x^7+423x^8+2724x^9+422x^10+128x^11+64x^12+46x^13+23x^14+4x^15+2x^16

The gray image is a code over GF(2) with n=72, k=12 and d=16.
This code was found by Heurico 1.16 in 0.00822 seconds.